Defeasible Logic versus Logic Programming without Negation as Failure

A clash of intuitions: The current state of nonmonotonic multiple inheritance systems. 13 6 Conclusion We have looked at the relationship between four logic programming-based formalisms that employ a priority relation among rules and take a sceptical approach to inference. Three, defeasible logic, LPwNF and courteous logic programs, belong to the same \school" while priority logic takes a fundamentally diierent approach, which is evident in its propagation of ambiguity. Of the three formalisms in the same school, defeasible logic is the most powerful. It is able to draw more conclusions (from the same rules) than LPwNF can, principally because it argues on the basis of teams of rules. Courteous logic programs also employ teams of rules, but the approach is severely restricted in that the atom dependency graph is required to be acyclic. In addition, of course, defeasible logic makes a distinction between deenite knowledge (obtained by facts and strict rules) and defeasible knowledge. These results indicate that defeasible logic deserves more attention. In other papers 2, 8] we have studied the logic as a formal system, including representation results, properties of the inference relation, and semantics. 12 It is worth mentioning that despite the underlying assumption of acyclicity, courteous logic programs are not a special case of LPwNF, because they do incorporate the idea of a team. For example, consider the program in example 3. mammal(platypus) can be proven in courteous logic programs, but not in LPwNF. Priority logic 12, 13] is a knowledge representation language where a theory consists of logic programming-like rules, and a priority relation among them. The meaning of the priority relation is that once a rule r is included in an argument, all rules inferior to r are automatically blocked from being included in the same argument. The semantics of priority logic is based on the notion of a stable argument for the credulous case, and the well-founded argument for the sceptical case. Priority logic is a general framework with many instantiations (based on so-called extensibility functions), and supports both credulous and sceptical reasoning. To allow a fair comparison to defeasible logic, one has to impose the following restrictions: (i) We will only consider defeasible rules in the sense of defeasible logic. That is, we will not distinguish between strict and defeasible rules, and we will restrict attention to rules in which only propositional literals occur (but not more general formulae, as in priority …